A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers ). More formally, given a number, define a sequence, , ... where is the sum of the squares of the digits of. Then n is happy if and only if there exists i such that . If a number is happy, then all members of its sequence are happy; if a number is unhappy, all members of the sequence are unhappy. For example, 19 is happy, as the associated sequence is: The 143 happy numbers up to 1,000 are: The happiness of a number is unaffected by rearranging the digits, and by inserting or removing any number of zeros anywhere in the number. https://en.wikipedia.org/wiki/Happy_number